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Spring 2014

White, Diana T

In this thesis, we construct a non-local transport model that describes the evolution of microtubules (MTs) as they interact with motor proteins. MTs, whose organization is crucial for normal cellular development, have been found to organize into various patterns in vitro and in vivo through...

Fall 2014

Slevinsky, Richard M

The numerical evaluation of challenging integrals is a topic of interest in applied mathematics. We investigate molecular integrals in the B function basis, an exponentially decaying basis with a compact analytical Fourier transform. The Fourier property allows analytical expressions for...

Fall 2014

Wai, Kevin

Financial systemic crisis could be broadly understood as the deterioration of the banking sector which results in damage to the real economy. From elementary accounting, a firm's financial position can be characterized by the value of its asset holdings versus the amount it borrow from others. If...

Spring 2014

Li, Hao

It is well known that the normal return estimation for financial asset prices is defective. In order to find better models to estimate the prices behavior of financial assets, people need probabilistic distribution that can capture fat-tails, non-constant moments, etc. This thesis find some...

Fall 2014

Conner, Patrick M

Among representation theorists, it is well known that Yangians can be realized as some type of degenerate form of quantum loop algebras. What is not well known is precisely how this degeneration takes place. In the first part of this thesis, we will demonstrate explicitly the process by which...

Fall 2014

Zhai, Zhichun

We study robust sampling designs for model-based stratification, when the assumed distribution F0 (·) of an auxiliary variable x, and the variance function g0 (·) in the associated regression model, are only approximately specified. We first maximize the scaled prediction mean squared error...

Spring 2014

Susanna, Spektor

This thesis is mostly based on six papers on selected topics in Asymptotic Geometric Analysis, Wavelet Analysis and Applied Fourier Analysis. The first two papers are devoted to Ball's integral inequality. We prove this inequality via spline functions. We also provide a method for computing all...

Spring 2014

Lin, Mu

We discuss non-parametric shape constrained density estimation methods in univariate setting and their applications to the classic Gaussian compound decision problem. The original contribution of the thesis is establishing various important consistency results of the shape constrained density...

Fall 2014

Lu, Boyuan

This thesis focuses on characterizing the optimal consumption and investment strategy for an investor, in a simple financial market, when his consumption habit is considered in the utility formulation. We consider a continuous-time market model for which we maximize the overall utility within an...

Fall 2014

Campbell, John J.

In this work we will construct the table of irreducible characters for the group of unitary 2 x 2 matrices over a finite field. The table and the methods for its construction will show interesting connections to the table and methods of construction of the table of irreducible characters for the...